A race driver has made a pit stop to refuel. After refueling,he leaves the pit a

Question

A race driver has made a pit stop to refuel. After refueling,he leaves the pit area with an acceleration whose magnitude is 5.87m/s2; after 4.14 s he enters the main speedway. At thesame instant, another car on the speedway and traveling at aconstant speed of 73.7 m/s overtakes and passes the entering car.If the entering car maintains its acceleration, how much time isrequired for it to catch the other car?
Could you find the distance covered by the entering car, andthen see how long it takes the car with the constant speed tocover that distance? A race driver has made a pit stop to refuel. After refueling,he leaves the pit area with an acceleration whose magnitude is 5.87m/s2; after 4.14 s he enters the main speedway. At thesame instant, another car on the speedway and traveling at aconstant speed of 73.7 m/s overtakes and passes the entering car.If the entering car maintains its acceleration, how much time isrequired for it to catch the other car?
Could you find the distance covered by the entering car, andthen see how long it takes the car with the constant speed tocover that distance?

Explanation / Answer

Just set the displacements of the two cars equal to one another,because this is when the entering car overtakes the other car, andsolve for the time of the entering car: First, however, we need the velocity of the entering car as it(haha) enters the speedway: Vf=Vi+at Vf=0+(5.87)(4.14) Vf= 24.3 m/s (the speed of entering car as it enters) Now set displacements equal: x=x (vit+.5at2)constant-vcar=(vit+.5at2)entering car (73.7t+0)=[24.3t+.5(5.87)(t2)] Set quadratic = to zero: 2.94t2-49.4t=0 Solve for t, which ends up being both 0 and 16.8 seconds. Sincezero is when the constant-velocity car overtakes the entering car,we disregard this answer. So 16.8 seconds is whenthe entering car overtakes the other car.

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